We study the recovery of functions in various norms, including L p Lₚ with 1 ≤ p ≤ ∞ 1 p, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best L 2 L₂ -approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case p = ∞ p=, our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces.
Krieg et al. (2025) studied this question.